Force-Field Functor Theory: Classical Force-Fields which Reproduce Equilibrium Quantum Distributions
Feynman and Hibbs were the first to variationally determine an effective potential whose associated classical canonical ensemble approximates the exact quantum partition function. We examine the existence of a map between the local potential and an effective classical potential which matches the exa...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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Frontiers Media S.A.
2013-10-01
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| Series: | Frontiers in Chemistry |
| Subjects: | |
| Online Access: | http://journal.frontiersin.org/Journal/10.3389/fchem.2013.00026/full |
| _version_ | 1818349378001174528 |
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| author | Ryan eBabbush John Anthony Parkhill Alan eAspuru-Guzik |
| author_facet | Ryan eBabbush John Anthony Parkhill Alan eAspuru-Guzik |
| author_sort | Ryan eBabbush |
| collection | DOAJ |
| description | Feynman and Hibbs were the first to variationally determine an effective potential whose associated classical canonical ensemble approximates the exact quantum partition function. We examine the existence of a map between the local potential and an effective classical potential which matches the exact quantum equilibrium density and partition function. The usefulness of such a mapping rests in its ability to readily improve Born-Oppenheimer potentials for use with classical sampling. We show that such a map is unique and must exist. To explore the feasibility of using this result to improve classical molecular mechanics, we numerically produce a map from a library of randomly generated one-dimensional potential/effective potential pairs then evaluate its performance on independent test problems. We also apply the map to simulate liquid para-hydrogen, finding that the resulting radial pair distribution functions agree well with path integral Monte Carlo simulations. The surprising accessibility and transferability of the technique suggest a quantitative route to adapting Born-Oppenheimer potentials, with a motivation similar in spirit to the powerful ideas and approximations of density functional theory. |
| first_indexed | 2024-12-13T18:05:00Z |
| format | Article |
| id | doaj.art-16bd4003568046a5a328d84f424cac86 |
| institution | Directory Open Access Journal |
| issn | 2296-2646 |
| language | English |
| last_indexed | 2024-12-13T18:05:00Z |
| publishDate | 2013-10-01 |
| publisher | Frontiers Media S.A. |
| record_format | Article |
| series | Frontiers in Chemistry |
| spelling | doaj.art-16bd4003568046a5a328d84f424cac862022-12-21T23:36:05ZengFrontiers Media S.A.Frontiers in Chemistry2296-26462013-10-01110.3389/fchem.2013.0002665852Force-Field Functor Theory: Classical Force-Fields which Reproduce Equilibrium Quantum DistributionsRyan eBabbush0John Anthony Parkhill1Alan eAspuru-Guzik2Harvard UniversityThe University of Notre DameHarvard UniversityFeynman and Hibbs were the first to variationally determine an effective potential whose associated classical canonical ensemble approximates the exact quantum partition function. We examine the existence of a map between the local potential and an effective classical potential which matches the exact quantum equilibrium density and partition function. The usefulness of such a mapping rests in its ability to readily improve Born-Oppenheimer potentials for use with classical sampling. We show that such a map is unique and must exist. To explore the feasibility of using this result to improve classical molecular mechanics, we numerically produce a map from a library of randomly generated one-dimensional potential/effective potential pairs then evaluate its performance on independent test problems. We also apply the map to simulate liquid para-hydrogen, finding that the resulting radial pair distribution functions agree well with path integral Monte Carlo simulations. The surprising accessibility and transferability of the technique suggest a quantitative route to adapting Born-Oppenheimer potentials, with a motivation similar in spirit to the powerful ideas and approximations of density functional theory.http://journal.frontiersin.org/Journal/10.3389/fchem.2013.00026/fullDensity Functional Theoryeffective potentialspath integral molecular dynamicsnuclear quantum propagationliquid hydrogen |
| spellingShingle | Ryan eBabbush John Anthony Parkhill Alan eAspuru-Guzik Force-Field Functor Theory: Classical Force-Fields which Reproduce Equilibrium Quantum Distributions Frontiers in Chemistry Density Functional Theory effective potentials path integral molecular dynamics nuclear quantum propagation liquid hydrogen |
| title | Force-Field Functor Theory: Classical Force-Fields which Reproduce Equilibrium Quantum Distributions |
| title_full | Force-Field Functor Theory: Classical Force-Fields which Reproduce Equilibrium Quantum Distributions |
| title_fullStr | Force-Field Functor Theory: Classical Force-Fields which Reproduce Equilibrium Quantum Distributions |
| title_full_unstemmed | Force-Field Functor Theory: Classical Force-Fields which Reproduce Equilibrium Quantum Distributions |
| title_short | Force-Field Functor Theory: Classical Force-Fields which Reproduce Equilibrium Quantum Distributions |
| title_sort | force field functor theory classical force fields which reproduce equilibrium quantum distributions |
| topic | Density Functional Theory effective potentials path integral molecular dynamics nuclear quantum propagation liquid hydrogen |
| url | http://journal.frontiersin.org/Journal/10.3389/fchem.2013.00026/full |
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